You can make any lossy compression scheme into a lossless scheme by appending the diff between the original and the compressed. In many cases, this still results in a size savings over the original.

You can think of this as a more detailed form of "I before E, except after C, except for species and science and..." Or, if you prefer, as continued terms of a Taylor-series expansion. The more terms you add, the more closely you approximate the original.

And just as fast? The issue here is how do you do these things both accurately and while maintaining reasonable speeds.